I find it somewhat unusual that one does not need to define electron coordinates in an electronic structure calculation. Taking Hartree Fock for example, the Fock operator includes the one-electron operator that depends on electron coordinate. However, the matrix representation of the Fock operator in the basis of $\{\phi_{\mu}\}$ is
$F_{\mu v}=\int d \mathbf{r}_{1} \phi_{\mu}^{*}(1) f(1) \phi_{v}(1)$
So because the entries in the Fock matrix are all integrals over all space $\int_{r_{1}=0}^{\infty} d \mathbf{r}_{1}$, it doesn't need the electron coordinate. Is that correct?